Can you solve the giant cat army riddle? - Dan Finkel
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Date: 2020-08-22
Comments and reviews: 6
Jessie
my solution:
(spoilers on read more)
to start, we want to get to 4, so we can sqrt that to get 2, but we cant do that, so we have to sqrt 16 to get 4. unfortunately, we cant get to 16 directly with 5 and 7, so we need to take another step. the easiest way to do this is to get to 6, and adding 10, but that requirs getting 36, which we can get with just 5 and 7.
our sequence so far looks like this.
5, 12, 17, 24, 29, 36, 6, 11, 16, 4, 2,
next we want to get to 10, the easiest way to do that is to get to 3 and then add 7, which can be done by adding 7, sqrting and then adding 7 again.
9, 3, 10,
then we want to get to 14. the easiest way to do this is getting to 7 and adding 7 again. the best way to get to 7 is by taking the root of 49. adding 7 twice and 5 the rest of the way gets us to the answer
15, 20, 25, 30, 35, 42, 49
we have 49, then just square root and add 7 you're free!
reply
my solution:
(spoilers on read more)
to start, we want to get to 4, so we can sqrt that to get 2, but we cant do that, so we have to sqrt 16 to get 4. unfortunately, we cant get to 16 directly with 5 and 7, so we need to take another step. the easiest way to do this is to get to 6, and adding 10, but that requirs getting 36, which we can get with just 5 and 7.
our sequence so far looks like this.
5, 12, 17, 24, 29, 36, 6, 11, 16, 4, 2,
next we want to get to 10, the easiest way to do that is to get to 3 and then add 7, which can be done by adding 7, sqrting and then adding 7 again.
9, 3, 10,
then we want to get to 14. the easiest way to do this is getting to 7 and adding 7 again. the best way to get to 7 is by taking the root of 49. adding 7 twice and 5 the rest of the way gets us to the answer
15, 20, 25, 30, 35, 42, 49
we have 49, then just square root and add 7 you're free!
reply
Arbitrary
I worked out the bonus riddle by doing a reverse breadth first search. Instead of getting from 11 to 25 with the operations x2 and -3, I went from 25 to 11 with the operations /2 and +3. The shortest solution to this can just be inverted to get the shortest solution to the original question. This simplifies the search space because when you run into odd numbers, you only have one option: +3. I was able to figure out all of the paths of length 3, then 4, then 5, then 6, then 7 by hand, eliminating all irrelevant paths that led me to a number I already visited. (For example, I found 25 28 31 34 17 to be one path, but I already had 25 28 14 17: since I already visited 17 in a shorter path, there's no way the longer one could provide an optimal solution)
I concluded that the fewest number of moves is seven. The path is 11, 8, 5, 10, 7, 14, 28, 25.
reply
I worked out the bonus riddle by doing a reverse breadth first search. Instead of getting from 11 to 25 with the operations x2 and -3, I went from 25 to 11 with the operations /2 and +3. The shortest solution to this can just be inverted to get the shortest solution to the original question. This simplifies the search space because when you run into odd numbers, you only have one option: +3. I was able to figure out all of the paths of length 3, then 4, then 5, then 6, then 7 by hand, eliminating all irrelevant paths that led me to a number I already visited. (For example, I found 25 28 31 34 17 to be one path, but I already had 25 28 14 17: since I already visited 17 in a shorter path, there's no way the longer one could provide an optimal solution)
I concluded that the fewest number of moves is seven. The path is 11, 8, 5, 10, 7, 14, 28, 25.
reply
Kuldeep
Bonus riddle answer.
8 presses to get to 25 from 11.
You're on 11, you press -3 twice.
You're on 5, you press x2 twice.
You're on 20, you press -3 twice.
You're on 14, you press x2 once.
You're on 28, you press -3 once.
You're on 25 now where you wanted to reach in 8 button press.
reply
Bonus riddle answer.
8 presses to get to 25 from 11.
You're on 11, you press -3 twice.
You're on 5, you press x2 twice.
You're on 20, you press -3 twice.
You're on 14, you press x2 once.
You're on 28, you press -3 once.
You're on 25 now where you wanted to reach in 8 button press.
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KoyasuNoBara
It's a good thing you didn't do 7 5 7 5 7 5 for the first part, or you'd be screwed when it came time to get to 14.
Maybe next time work out the _entire_ solution before you press buttons so that you don't have to rely on luck.
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It's a good thing you didn't do 7 5 7 5 7 5 for the first part, or you'd be screwed when it came time to get to 14.
Maybe next time work out the _entire_ solution before you press buttons so that you don't have to rely on luck.
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Shantari
I reached my solution a bit differently. I started from 2 and finished the sequence, before finding how to get 2. I figured that way i could more easily see which numbers not to repeat.
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I reached my solution a bit differently. I started from 2 and finished the sequence, before finding how to get 2. I figured that way i could more easily see which numbers not to repeat.
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Yuya
And for the bonus riddle I got, 11, 8, 5, 10, 20, 17, 14, 28, 25, which is 8 operations, don't know if it is the smallest possible route though.
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And for the bonus riddle I got, 11, 8, 5, 10, 20, 17, 14, 28, 25, which is 8 operations, don't know if it is the smallest possible route though.
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